All characters start with 10 AC, plus Dexterity, without armor. Armor that a character puts on changes the base number from 10 to some other higher number (like 11 for Leather armor), and may modify how Dexterity applies.

For example, here is a selection of armor, their base AC, and dexterity modifiers

Yea? Under what pdf cause I didn't see anything under classes, equiptment , how to play or in the dm guidelines. Your assumption that I did not read the material is fallacious, its alot to digest for some one who is new to the game and learning to Dm first and player character second.

Yea? Under what pdf cause I didn't see anything under classes, equiptment , how to play or in the dm guidelines. Your assumption that I did not read the material is fallacious, its alot to digest for some one who is new to the game and learning to Dm first and player character second.

How to Play, page 21 under 'spell components'.

use ctrl+f to search a pdf document. i just searched 'casting' and found the necessary info in less than a minute.

Somatic components. In this edition, you need one hand free to cast arcane spells. That prevents the wizard from using a shield. Besides that, they are not proficient and it would be detrimental to them to wield it.

In terms of weapons that wizards can use, what is stopping them from using a sheild and sword and still using magic?

First, the wizard has no proficiency in either shields or longswords. You can view their proficiencies in the Classes document, page 25 under "Armor and Shield Proficiencies" and "Weapon Proficiencies" (these are at the top of the page in the second column). The use of these items without proficiency would yield penalties to the character.

Secondly, it is as Lord Kyrion said, you need at least 1 free hand to cast spells that require Somatic Components (i.e. hand waving and finger jiggling). The caveat to the "one hand free" rule, as far as I can see, is that you can still wield 2-handed weapons (like the quarterstaff) and are still able to cast spells.

From document "How to Play", page 21

If you can’t complete a spell’s components, you are unable to cast the spell. Thus, if you are silenced or don’t have a hand free, you cannot cast a spell.

However if you take a Hill Dwarf you get more Hit points, or take a Mountain Dwarf you can wear armour. - This may lead to many Dwarf wizards, which is a contrast to previous editions but hey, could be very cool. Proof's in the pudding as they say.

You could take Sharpshooter specialty for the Sniper feat, allowing use of Long Bows and fire at enemies at a distance (better range than Light Crossbows)

You could take the Ambusher specialty for the Improved Initiative feat, and simply act before your enemies.

Key things for D&D - Where is the character from and why do they do what they do? / Recurring NPCs - allies and enemies / Plot, World and Personal Events.